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Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity
1. | University of Vienna, Fakultät für Mathematik, Nordbergstraße 15, 1090 Vienna |
References:
[1] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[2] |
A. Constantin, Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train, Eur. J. Mech. B Fluids, 30 (2011), 12-16.
doi: 10.1016/j.euromechflu.2010.09.008. |
[3] |
A. Constantin, "Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis," CBMS-NSF Series in Applied Mathematics, Vol. 81, SIAM, Philadelphia, 2011. |
[4] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603.
doi: 10.1215/S0012-7094-07-14034-1. |
[5] |
A. Constantin and J. Escher, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech., 498 (2004), 171-181.
doi: 10.1017/S0022112003006773. |
[6] |
A. Constantin and J. Escher, Particle trajectories in solitary water waves, Bull. Amer. Math. Soc., 44 (2007), 423-431.
doi: 10.1090/S0273-0979-07-01159-7. |
[7] |
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 173 (2011), 559-568.
doi: 10.4007/annals.2011.173.1.12. |
[8] |
A. Constantin, J. Escher and H.-C. Hsu, Pressure beneath a solitary water wave: mathematical theory and experiments, Arch. Rational Mech. Anal., 201 (2011), 251-269.
doi: 10.1007/s00205-011-0396-0. |
[9] |
A. Constantin, D. Sattinger and W. Strauss, Variational formulations for steady water waves with vorticity, J. Fluid Mech., 548 (2006), 151-163.
doi: 10.1017/S0022112005007469. |
[10] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481-527.
doi: 10.1002/cpa.3046. |
[11] |
A. Constantin and W. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., 60 (2007), 911-950.
doi: 10.1002/cpa.20165. |
[12] |
A. Constantin and W. Strauss, Rotational steady water waves near stagnation, Philos. Trans. Roy. Soc. London A, 365 (2007), 2227-2239.
doi: 10.1098/rsta.2007.2004. |
[13] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557. |
[14] |
A. Constantin and W. Strauss, Periodic traveling gravity water waves with discontinuous vorticity, Arch. Rational Mech. Anal., 202 (2011), 133-175.
doi: 10.1007/s00205-011-0412-4. |
[15] |
A. Constantin and E. Varvaruca, Steady periodic water waves with constant vorticity: regularity and local bifurcation, Arch. Rational Mech. Anal., 199 (2011), 33-67.
doi: 10.1007/s00205-010-0314-x. |
[16] |
A. F. Teles da Silva and D. H. Peregrine, Steep, steady surface waves on water of finite depth with constant vorticity, J. Fluid Mech., 195 (1988), 281-302.
doi: 10.1017/S0022112088002423. |
[17] |
M. Ehrnström, On the streamlines and particle paths of gravitational water waves, Nonlinearity, 21 (2008), 1141-1154.
doi: 10.1088/0951-7715/21/5/012. |
[18] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[19] |
M. Goldshtik and F. Hussain, Inviscid separation in steady planar flows, Fluid Dynamics Research, 23 (1998), 235-266.
doi: 10.1016/S0169-5983(98)00017-3. |
[20] |
D. Henry, Particle trajectories in linear periodic capillary and capillary-gravity water waves, Philos. Trans. Roy. Soc. London A, 365 (2007), 2241-2251.
doi: 10.1098/rsta.2007.2005. |
[21] |
D. Henry, Steady periodic waves bifurcating for fixed-depth rotational flows,, Quart. Appl. Math. (in print)., ().
|
[22] |
I. G. Jonsson, Wave-current interactions, in "The Sea" (eds. B. Le Mehaute and D. M. Hanes), J. Wiley, (1990), 65-120. |
[23] |
J. Ko and W. Strauss, Effect of vorticity on steady water waves, J. Fluid Mech., 608 (2008), 197-215.
doi: 10.1017/S0022112008002371. |
[24] |
J. Ko and W. Strauss, Large-amplitude steady rotational water waves, Eur. J. Mech. B Fluids, 27 (2008), 96-109.
doi: 10.1016/j.euromechflu.2007.04.004. |
[25] |
D. H. Peregrine, Interaction of water waves and currents, Adv. Appl. Mech., 16 (1976), 9-117.
doi: 10.1016/S0065-2156(08)70087-5. |
[26] |
V. V. Prasolov, "Polynomials," Springer -Verlag, Berlin-Heidelberg, 2010. |
[27] |
W. A. Strauss, Steady water waves, Bull. Amer. Math. Soc. (N.S.), 47 (2010), 671-694. |
[28] |
C. Swan, I. Cummins and R. James, An experimental study of two-dimensional surface water waves propagating on depth-varying currents, J. Fluid Mech., 428 (2001), 273-304.
doi: 10.1017/S0022112000002457. |
[29] |
G. Thomas and G. Klopman, Wave-current interactions in the nearshore region, in "Gravity Waves in Water of Finite Depth," Advances in Fluid Mechanics, Wessex Institute of Technology, Southhampton (1997), 215-319. |
[30] |
J.-P. Tignol, "Galois' Theory of Algebraic Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 2001. |
[31] |
E. Varvaruca, On some properties of traveling water waves with vorticity, SIAM J. Math. Anal., 39 (2008), 1686-1692.
doi: 10.1137/070697513. |
[32] |
E. Wahlén, Steady water waves with a critical layer, J. Differential Equations, 246 (2009), 2468-2483.
doi: 10.1016/j.jde.2008.10.005. |
show all references
References:
[1] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
[2] |
A. Constantin, Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train, Eur. J. Mech. B Fluids, 30 (2011), 12-16.
doi: 10.1016/j.euromechflu.2010.09.008. |
[3] |
A. Constantin, "Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis," CBMS-NSF Series in Applied Mathematics, Vol. 81, SIAM, Philadelphia, 2011. |
[4] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603.
doi: 10.1215/S0012-7094-07-14034-1. |
[5] |
A. Constantin and J. Escher, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech., 498 (2004), 171-181.
doi: 10.1017/S0022112003006773. |
[6] |
A. Constantin and J. Escher, Particle trajectories in solitary water waves, Bull. Amer. Math. Soc., 44 (2007), 423-431.
doi: 10.1090/S0273-0979-07-01159-7. |
[7] |
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 173 (2011), 559-568.
doi: 10.4007/annals.2011.173.1.12. |
[8] |
A. Constantin, J. Escher and H.-C. Hsu, Pressure beneath a solitary water wave: mathematical theory and experiments, Arch. Rational Mech. Anal., 201 (2011), 251-269.
doi: 10.1007/s00205-011-0396-0. |
[9] |
A. Constantin, D. Sattinger and W. Strauss, Variational formulations for steady water waves with vorticity, J. Fluid Mech., 548 (2006), 151-163.
doi: 10.1017/S0022112005007469. |
[10] |
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481-527.
doi: 10.1002/cpa.3046. |
[11] |
A. Constantin and W. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., 60 (2007), 911-950.
doi: 10.1002/cpa.20165. |
[12] |
A. Constantin and W. Strauss, Rotational steady water waves near stagnation, Philos. Trans. Roy. Soc. London A, 365 (2007), 2227-2239.
doi: 10.1098/rsta.2007.2004. |
[13] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557. |
[14] |
A. Constantin and W. Strauss, Periodic traveling gravity water waves with discontinuous vorticity, Arch. Rational Mech. Anal., 202 (2011), 133-175.
doi: 10.1007/s00205-011-0412-4. |
[15] |
A. Constantin and E. Varvaruca, Steady periodic water waves with constant vorticity: regularity and local bifurcation, Arch. Rational Mech. Anal., 199 (2011), 33-67.
doi: 10.1007/s00205-010-0314-x. |
[16] |
A. F. Teles da Silva and D. H. Peregrine, Steep, steady surface waves on water of finite depth with constant vorticity, J. Fluid Mech., 195 (1988), 281-302.
doi: 10.1017/S0022112088002423. |
[17] |
M. Ehrnström, On the streamlines and particle paths of gravitational water waves, Nonlinearity, 21 (2008), 1141-1154.
doi: 10.1088/0951-7715/21/5/012. |
[18] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[19] |
M. Goldshtik and F. Hussain, Inviscid separation in steady planar flows, Fluid Dynamics Research, 23 (1998), 235-266.
doi: 10.1016/S0169-5983(98)00017-3. |
[20] |
D. Henry, Particle trajectories in linear periodic capillary and capillary-gravity water waves, Philos. Trans. Roy. Soc. London A, 365 (2007), 2241-2251.
doi: 10.1098/rsta.2007.2005. |
[21] |
D. Henry, Steady periodic waves bifurcating for fixed-depth rotational flows,, Quart. Appl. Math. (in print)., ().
|
[22] |
I. G. Jonsson, Wave-current interactions, in "The Sea" (eds. B. Le Mehaute and D. M. Hanes), J. Wiley, (1990), 65-120. |
[23] |
J. Ko and W. Strauss, Effect of vorticity on steady water waves, J. Fluid Mech., 608 (2008), 197-215.
doi: 10.1017/S0022112008002371. |
[24] |
J. Ko and W. Strauss, Large-amplitude steady rotational water waves, Eur. J. Mech. B Fluids, 27 (2008), 96-109.
doi: 10.1016/j.euromechflu.2007.04.004. |
[25] |
D. H. Peregrine, Interaction of water waves and currents, Adv. Appl. Mech., 16 (1976), 9-117.
doi: 10.1016/S0065-2156(08)70087-5. |
[26] |
V. V. Prasolov, "Polynomials," Springer -Verlag, Berlin-Heidelberg, 2010. |
[27] |
W. A. Strauss, Steady water waves, Bull. Amer. Math. Soc. (N.S.), 47 (2010), 671-694. |
[28] |
C. Swan, I. Cummins and R. James, An experimental study of two-dimensional surface water waves propagating on depth-varying currents, J. Fluid Mech., 428 (2001), 273-304.
doi: 10.1017/S0022112000002457. |
[29] |
G. Thomas and G. Klopman, Wave-current interactions in the nearshore region, in "Gravity Waves in Water of Finite Depth," Advances in Fluid Mechanics, Wessex Institute of Technology, Southhampton (1997), 215-319. |
[30] |
J.-P. Tignol, "Galois' Theory of Algebraic Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 2001. |
[31] |
E. Varvaruca, On some properties of traveling water waves with vorticity, SIAM J. Math. Anal., 39 (2008), 1686-1692.
doi: 10.1137/070697513. |
[32] |
E. Wahlén, Steady water waves with a critical layer, J. Differential Equations, 246 (2009), 2468-2483.
doi: 10.1016/j.jde.2008.10.005. |
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